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تسجيل مستخدم جديدSub-Riemannian Ricci curvature via generalized Gamma $z$ calculus
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We derive sub-Riemannian Ricci curvature tensor for sub-Riemannian manifolds. We provide examples including the Heisenberg group, displacement group ($textbf{SE}(2)$), and Martinet sub-Riemannian structure with arbitrary weighted volumes, in which we establish analytical bounds for sub-Riemannian curvature dimension bounds and log-Sobolev inequalities. {These bounds can be used to establish the entropy dissipation results for sub-Riemannian drift diffusion processes on a compact spatial domain, in term of $L_1$ distance.} Our derivation of Ricci curvature is based on generalized Gamma $z$ calculus and $z$--Bochners formula, where $z$ stands for extra directions introduced into the sub-Riemannian degenerate structure.
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